James Willstrop, the world's best squash player, is rarely noticed away from the glass courts of his brutal trade. He might be one of the most intriguing and driven competitors in British sport but the diffident disciple of Oscar Wilde mocks his enduring anonymity with a wry story.

"I enjoy being alone," Willstrop says quietly as he begins an anecdote which bears the deft touch of the writer he has become while rising to his current position as the world No1. "So it was amusing when I got a taste of fame. I went to see One Man & Two Guvnors at the Theatre Royal Haymarket and ended up imagining myself as Andy Murray."

Willstrop laughs on a beautiful afternoon in Nuremberg, where he is in the midst of leading England to their annual title as European champions alongside Nick Matthew, the world No2 and his contrasting nemesis and fellow Yorkshireman. The gripping struggle between Willstrop and Matthew should be one of the stories of the Olympic Games this summer – except for the fact that their sport continues to be ignored by the IOC.

Squash is played in 150 countries around the world and it conveys the accessibility and purity of sport in graphic terms. Yet the IOC has either blocked the claims of squash or insisted golf and rugby sevens are more attuned to its Olympic ideals. It's little wonder that Willstrop is happier talking about his most recent visit to the theatre.

"I was on my own in London as Vanessa [Atkinson, the former world No1 squash player who is his girlfriend] was away. As there was no reason to rush home to Leeds, I went to the theatre. I made the mistake of buying a front-row seat and got picked out for some audience participation – my worst nightmare. But, even though I'm shy, I'm a bit of a showman deep inside. So up I went on stage, as one of Britain's few world No1s, and no one had a clue.

"If they'd asked me what I did I might've lied. I think it would have spun them out if I said I played squash for a living and, actually, I'm ranked one in the world. I preferred the fact that I was treading the boards where Wilde's first comedy [A Woman Of No Importance] was staged.

"I got through 10 minutes of mickey-taking with Owain Arthur – who was brilliant in the lead role – and at the interval I needed a drink. Suddenly, people were staring and pointing at me. Andy Murray must feel like that whenever he goes out. Life would be much more difficult if I had to deal with that constant scrutiny."

Willstrop, who offers engaging company, can be solitary and contradictory. But he brings a fierce insight and literary edge to his draining world. His first book, Shot And A Ghost, is one of the sporting reads of the year, a deeply personal and poignant account of life on tour and the grief he still feels after the death of his mother when he was 16. The book's publication has coincided with his surge to world No1.

"Writing it has made me a better player," he says. "It's helped me put down some painful thoughts and, as I was reaching the culmination, I began winning one big event after another. The first tournament was in Hong Kong when I was in the final stages of writing and redrafting. I remember winning matches and, straightaway, heading off to a cafe to write."

Willstrop concentrates hard as he tries to voice the emotions that took hold of him, last December, when he became world No1. "It was in Delhi and the actual night was magical," he murmurs. "You sit there and wonder why it feels so good. All you can say is 'unbelievable …' It came at the end of a particularly brutal match against Grégory Gaultier.

"The first game lasted 57 minutes – and I lost it. But I felt strong. The second game was also tight but I edged it. I ran away from him in the third and in the fourth he retired with severe cramp when I was 4-1 up. It was a tremendous mental effort.

"I went to the floor. Remember how Mo Farah went down on the track after he won? I was like that. The achievement in itself is monumental – to be the best in the world. But I was more overwhelmed by the time we had invested over so many years. It took so long to reach that point, from so many people who made it happen."

The man who had done most to drive Willstrop was also in Delhi. Malcolm Willstrop, James's father and maverick coach, has been intimately involved in this slow rise from the courts of Pontefract to the pinnacle of squash. "Dad's the Brian Clough of squash," Willstrop shrugs. "He's brilliant but an extremely different character. That eccentricity makes him special."

It also makes him difficult and, after their emotional night in Delhi with Vanessa and James's half-brother, David, a coach on the British team, Malcolm Willstrop has withdrawn from his son. "It's not been easy," Willstrop says. "India knocked the hell out of him. He had visa troubles and as soon as we got back he fell ill with an infection. It was such a big achievement it's almost been too much for him to absorb. He's needed some time alone because it's been heavy. The intensity took so much out of him – because you work your whole life towards this goal and, when it happens, you have to realign yourself.

"We had a couple of issues after I became world No1 when he went into his shell. It was his way of saying, 'I need to get over this …' All through January we didn't say much to each other. I felt it was best to leave him to deal with whatever he's dealing with. It's resolved itself but he's so different we'll always have these issues. I'm not the easiest person in the world either. He has to deal with my doubts and intensities. I just hope we see him at the British Open."

Next Monday, at London's O2, on the edge of the Olympic heartland, the British Open will showcase the absorbing rivalry between Willstrop and Matthew – as well as Ramy Ashour, Egypt's feted young magician of the court. It will also ask the perplexing question as to why the IOC shuns squash – especially in this London Olympic year when Britain supplies the world's two best players. "Our worst disappointment came in 2005," Willstrop says, "when we came so close to being included in London 2012. They had removed two sports but chose not to vote in any replacements. So I wasn't surprised when, voting for 2016, they went for golf and rugby sevens. Golfers have huge fame and wealth and that drew the IOC – which also decided rugby sevens would fill some arenas."

As the sport strives to be included in 2020, Willstrop extols the virtues of squash. "It's tailor-made for the Olympics. Squash has so many dimensions – speed, endurance, flexibility, agility, skill and psychology. It's accessible and inclusive. I wish they'd see us in a stark setting like this, in Nuremberg, where small countries get a chance. I'm not really a team-man but I love this competition because some years we've had amateurs from the Isle of Man or Estonia next to the world No1.

"Squash is played all over the world and yet 90 men sit in a hall and vote us out. I don't know what more the IOC wants from us because we've got as many Olympic attributes as any other sport. I don't think the world's top golfers will care about the Olympics and, let's face it, there's an inaccessibility about golf. They didn't let women on to some courses until recently."

Willstrop smiles thinly, but his incomprehension and hurt is plain. "It would've been incredible to be part of London 2012. You're seeing all the publicity Olympic sportsmen and women are getting and it reminds you how close we came. It would be wonderful to bask in that recognition. But we'll just be watching TV at home this summer. I love the fact that low-profile but incredible people, like Sarah Stevenson in taekwondo, are on this great stage. I just wish we could also be there."

Later, at lunch, we are joined by his friend, Jenny Duncalf. After five minutes of amiable chit-chat I ask her what she is doing in Nuremberg. Willstrop laughs gently. "Jenny's No2 in the world," he explains. My embarrassed apologies are handled graciously by Duncalf. "I don't expect you to know me," she smiles.

Yet she and her contemporaries in world squash should not be so cruelly anonymous. An Olympic final between Willstrop and Matthew, after all, would provide sporting drama at its most compelling. "It would have been incredible," Willstrop sighs. "People love animosity and there've been difficulties between me and Nick. Things have been said and we're very different. We don't have much to do with each other outside squash and people are captivated. But he's a great player and our rivalry is really interesting.

"Nick was No1 for a long time and then, in January, I took over. He beat me in February and got it back and then, in March, I was determined at this big tournament in Richmond [Virginia]. I had a blinder and beat Ramy 3-0 in the final. It was one of my most accomplished performances and all the sweeter because I'm No1 again."

Does Matthew himself believe Willstrop is the world's best player? "Probably not. At 31, he's at his peak. I'm 28 and getting better all the time but his game has stifled me at times. Nick has had it over me quite substantially. He's won our last 16 or 17 matches. That's a lot and he's 30-odd to 15 ahead. He's been on this run against me because, for two years, he was the best in the world. But I'm now No1."

Does his losing-streak carry some psychological baggage? "I really don't think so," Willstrop says. "None of them have been devastating losses and he was beating everyone else as well. I look at my defeats sensibly and realise I've played very well against Nick. I'm ready to beat him again."

Willstrop leans forward and, speaking in a way that would not be matched by an Olympic golfer or rugby sevens player, reflects on the bruising artistry of his sport. "I like to win but I remember a heavy two-hour match Nick and I played at Canary Wharf in 2010. It was amazing squash and I was more proud than disappointed. Nick and I shared something that is still talked about today. I love it when people come up and say how our match affected them. I appreciate art; and sport, like in that match, is a form of art. That artistry inspires and involves people. It would have made a perfect fit for the Olympics this year."

A Shot and a Ghost: A year in the brutal world of professional squash is available from www.willstrop.co.uk, £9.99